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Simulated annealing and quantum detailed balance. (English) Zbl 0716.47039
Summary: The analogue of simulated annealing is considered for time-inhomogeneous evolutions of a von Neumann algebra of operators, whose instantaneous generator at each time t satisfies the quantum detailed balance condition with respect to a faithful normal state which depends on time through a suitable cooling schedule. Convergence to the (nonfaithful) limiting state is proved under the usual kinds of assumptions. The approach is interesting in view of possible applications to stochastic Ising models and to Boltzmann machines.

MSC:
47N55 Applications of operator theory in statistical physics (MSC2000)
82B10 Quantum equilibrium statistical mechanics (general)
46N55 Applications of functional analysis in statistical physics
46L51 Noncommutative measure and integration
46L53 Noncommutative probability and statistics
46L54 Free probability and free operator algebras
46L60 Applications of selfadjoint operator algebras to physics
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